Busboom A, Lüke H D
Appl Opt. 2001 Aug 10;40(23):3894-900. doi: 10.1364/ao.40.003894.
Two-dimensional binary signals (arrays) with good autocorrelation properties are needed for coded-aperture imaging systems. In many astrophysical instruments, circular detectors with hexagonally packed detector elements are used, such that hexagonal coded apertures are often preferable to rectangular ones. A general method for folding a one-dimensional sequence into a hexagonal array is presented, by which the periodic or odd-periodic correlation properties of the original sequence are preserved. This method is applied to a known family of sequences with perfect odd-periodic correlation, yielding a new family of almost-binary and odd-perfect-or binary and almost odd-perfect-hexagonal arrays with optimum properties for coded-aperture imaging. The new odd-perfect arrays have near-uniform side lengths and exist for many more sizes than known families of even-periodic hexagonal arrays with good imaging properties.
编码孔径成像系统需要具有良好自相关特性的二维二进制信号（阵列）。在许多天体物理仪器中，使用具有六边形排列探测器元件的圆形探测器，因此六边形编码孔径通常比矩形编码孔径更可取。本文提出了一种将一维序列折叠成六边形阵列的通用方法，该方法可保留原始序列的周期性或奇周期性相关特性。该方法应用于一个具有完美奇周期相关性的已知序列族，得到了一个新的几乎二进制和奇完美或二进制和几乎奇完美六边形阵列族，具有编码孔径成像的最佳特性。新的奇完美阵列具有近乎均匀的边长，并且与具有良好成像特性的已知偶周期六边形阵列族相比，存在更多的尺寸。
